NEEDHAM, AUG. 21, 2014…..The two Democrats running to replace Attorney General Martha Coakley on Thursday raised questions about a civil settlement her office recently reached with a lobbying firm.

Both prefaced criticism by saying it was based on what they had read in published reports about the settlement, with Maura Healey, a former prosecutor who worked for Coakley until late last year, stating Coakley didn’t go far enough in the case, and former Sen. Warren Tolman saying he had concerns “at first blush.”

Republican John Miller, a Winchester attorney, is also running for attorney general, an open position because Coakley is running for governor. His camp said the settlement was “direct evidence” of how Democrat-dominated Beacon Hill “just isn’t getting the job done.”

Coakley’s office said last week it had reached a settlement with the Brennan Group in which the firm would pay $100,000 over three years to the Franciscan Hospital for Children and avoid civil or criminal charges. The firm had been paid $370,855 under an allegedly improper contract.

Coakley’s office has contended that the company collected fees illegally contingent on the firm’s success on winning state funding for the hospital, and argued there were “significant impediments” to going ahead with criminal prosecution, including issues with the statute of limitations, a lack of legal precedent and the credibility of a key witness.

“Maura can have her opinion, but she is just wrong on this,” said Brad Puffer, a Coakley spokesman. “This action was the right result based on the facts, and resulted in $100,000 being returned back to the charity when we risked getting nothing. Attorney General Coakley is going to continue to step up, make tough decisions, and work to get results for people.”

Treasurer Steve Grossman, one of Coakley’s Democratic rivals in the race for governor, has also criticized Coakley’s handling of the case, and on Wednesday, Secretary of State William Galvin, whose office oversees lobbyists, launched his own inquiry.

Healey and Tolman are competing in the Democratic primary on Sept. 9, and the winner will face Miller in November.

“I think it’s incredibly important that when there are allegations of corruption or fraud on the system, illegal lobbying activities, you absolutely take them on, you investigate them and you hold people accountable for not playing by the rules,” Healey told reporters on Thursday. “It is incredibly important. Now based on the reports and what I’ve read today, I don’t think the attorney general went far enough.”

Tolman also couched his comments by saying he had read about the case. “I don’t know the facts here,” he said. “It’s cause for concern, frankly. And I don’t want to say yes, no, or maybe, because it may be — who knows what happens with the secretary of state’s [inquiry].”

Citing reports on the settlement in the Boston Globe and Herald, Galvin’s chief legal counsel on Wednesday wrote to John Brennan, the president of the Brennan Group and a former state senator, apprising him of the secretary of state’s inquiry.

“This office requests that you immediately review all registration and disclosure reports from 2002 through 2008 and make any necessary corrections and amendments,” Laurie Flynn, the chief legal counsel, wrote. “Additionally, please provide copies of any and all contracts, billing statements and other documentation in your possession related to services rendered, work performed or compensation received in connection with executive or legislative lobbying on behalf of the Franciscan Hospital for Children.”

Asked for comment on Thursday, former Sen. Brennan pointed to a statement released by his firm, which said it had consented to the settlement without any admission of wrongdoing and “vigorously denies any violation of law.”

The firm provided lobbying and consulting services to the hospital when it was “facing significant financial problems and we worked with them to restructure some of their financing and develop a plan to help resolve their financial problems going forward,” the Brennan Group said.

The firm said that Coakley’s office claimed illegal contingency payments based on an agreement that was more than 10 years old, and both the firm and her office “acknowledged that there is an absence of clear legal precedent on matters of this type.”

The firm continues to believe the claims of Coakley’s office are “without merit,” but the settlement allows “our company to put this matter behind us and prevents further distractions,” the statement added. “We are pleased to have resolved this issue without any admission of wrongdoing, sanctions, or penalties,” it said.

After sparring with Healey at a WCVB-TV debate set to air on Sunday, Tolman told reporters in the TV station’s lobby that he is familiar with the hospital because he has a niece who spent “an awful lot of time” there. The hospital is also located within his former state Senate district.

When pressed for his thoughts on whether Coakley handled the matter correctly, Tolman added, “You’ve got to balance that with statute of limitations issues. And obviously I don’t know when this was brought to her attention, how quickly they could move or anything. These are all issues that are out there that I don’t want to be a Monday morning quarterback, when I don’t have all the facts.”

Asked later about a June 2014 campaign donation to Tolman by Brennan, Tolman’s campaign manager, Chris Joyce, reiterated the candidate’s concerns about the settlement and said he has a “strong record” of taking on special interests.

“He believes that anyone who takes advantage of an organization like this should be held accountable,” Joyce said in a statement. “Warren understands that the Secretary of State is looking into the matter to determine whether additional civil penalties are warranted, and he supports that action.”

Healey, who did not work on the case while employed in the attorney general’s office, broke with her former boss, Coakley, and said she was independent from “Beacon Hill politics.”

“This is a situation where somebody is taking a cut, skimming funds from funds that are supposed to go to an organization that serves poor kids,” she said. “So, you know, these kinds of allegations, anything that sounds in violations of ethics, of existing laws, corruption, fraud on the system, it is incredibly important that we investigate and pursue them vigorously, and I certainly will as attorney general, and I bring an independence to it and an ability to make sure that that happens.”

A spokesman for Miller, the Republican candidate, said he was concerned about Coakley’s office citing the statute of limitations.

“John has dealt with similar situations over the past 36 years of law practice. The parties simply agree to toll (or suspend) the statute of limitations,” Rick Gorka, the spokesman, said in a statement. “This gives them time to reach the right result. If one party won’t agree, formal proceedings are commenced. Here, it looks like both the AG and The Brennan Group wanted to avoid formal proceedings. When John is AG, such a settlement will not be at the expense of a more favorable outcome for a children’s hospital.”